Fractal geometry based model for a musical cymbal design and rapid manufacturing

This paper aims at an equation based simulation, CAD modeling and manufacturing of a fractal surface embedded on a musical cymbal. This study is essentially a proof-of-concept of a new method of complex-surface characterization, design and manufacturing using an equation-based approach. A cymbal shape was chosen to carry the fractal profile because generally most musical cymbals have an inherent broken surface pattern that is created to enhance the resulting musical quality, and hence it would be a topic of further study to characterize the musical notes emanating from a fractal surface on this cymbal. A fractal surface cymbal model was developed; a point cloud representation of the cymbal was generated from Matlab; a surface model was built and processed in image data processing software Imageware; a solid model was completed in CAD software PRO/E; a rapid prototype of the fractal surface cymbal was fabricated; and MasterCam software was used to generate CNC codes and simulate the CNC machining process. The effect of the variation of the parameters of the equation based surface is also shown by varying the topothesy and fractal parameter of the surface. Finally, the equation based method is used to generate other complex surfaces such as Cassini surface and the Bohemian Dome which are then solidified and prepared of manufacture.